Diminished family: Difference between revisions
m Moving from Category:Rank-2 to Category:Rank 2 using Cat-a-lot |
→Diminished: copy from jubilismic clan |
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== Diminished == | == Diminished == | ||
[[Subgroup]]: 2.3.5.7 | |||
Subgroup: 2.3.5.7 | |||
[[Comma list]]: 36/35, 50/49 | [[Comma list]]: 36/35, 50/49 | ||
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{{Multival|legend=1|4 4 4 -3 -5 -2}} | {{Multival|legend=1|4 4 4 -3 -5 -2}} | ||
[[POTE | [[Optimal tuning]] ([[POTE]]): ~6/5 = 1\4, ~3/2 = 699.523 | ||
{{Val list|legend=1| 4, 8d, 12 }} | {{Val list|legend=1| 4, 8d, 12 }} | ||
[[Badness]]: 0.022401 | [[Badness]]: 0.022401 | ||
=== 11-limit === | |||
Subgroup: 2.3.5.7.11 | |||
Comma list: 36/35, 50/49, 56/55 | |||
Mapping: [{{val| 4 0 3 5 14 }}, {{val| 0 1 1 1 0 }}] | |||
Optimal tuning (POTE): ~6/5 = 1\4, ~3/2 = 709.109 | |||
Optimal GPV sequence: {{Val list| 4, 8d, 12, 32cddee, 44cddeee }} | |||
Badness: 0.022132 | |||
Scales: [[diminished12]] | |||
==== 13-limit ==== | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 36/35, 40/39, 50/49, 66/65 | |||
Mapping: [{{val| 4 0 3 5 14 15 }}, {{val| 0 1 1 1 0 0 }}] | |||
Optimal tuning (POTE): ~6/5 = 1\4, ~3/2 = 713.773 | |||
Optimal GPV sequence: {{Val list| 4, 8d, 12f, 20cdef }} | |||
Badness: 0.019509 | |||
Scales: [[diminished12]] | |||
=== Demolished === | |||
Subgroup: 2.3.5.7.11 | |||
Comma list: 36/35, 45/44, 50/49 | |||
Mapping: [{{val| 4 0 3 5 -5 }}, {{val| 0 1 1 1 3 }}] | |||
Optimal tuning (POTE): ~6/5 = 1\4, ~3/2 = 689.881 | |||
Optimal GPV sequence: {{Val list| 12, 28, 40de }} | |||
Badness: 0.026574 | |||
=== Cohedim === | |||
This temperament has been documented in Graham Breed's temperament finder as ''hemidim'', the same name as [[Dimipent family #Hemidim|11-limit 4e & 24 and 13-limit 4ef & 24]]. For 11-limit 8bce & 12 temperament, ''cohedim'' arguably makes more sense. | |||
Subgroup: 2.3.5.7.11 | |||
Comma list: 36/35, 50/49, 125/121 | |||
Mapping: [{{val| 4 1 4 6 6 }}, {{val| 0 2 2 2 3 }}] | |||
Mapping generators: ~6/5, ~11/7 | |||
Optimal tuning (POTE): ~6/5 = 1\4, ~12/11 = 101.679 | |||
Optimal GPV sequence: {{Val list| 8bce, 12 }} | |||
Badness: 0.054965 | |||
==== 13-limit ==== | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 36/35, 50/49, 66/65, 125/121 | |||
Mapping: [{{val| 4 1 4 6 6 7 }}, {{val| 0 2 2 2 3 3 }}] | |||
Optimal tuning (POTE): ~6/5 = 1\4, ~12/11 = 102.299 | |||
Optimal GPV sequence: {{Val list| 8bcef, 12f }} | |||
Badness: 0.041707 | |||
== Hemidim == | == Hemidim == | ||